Counting of Number . Place Values Roman Figures
Subject :
Mathematics
Term :
First Term
Week:
Week One
Class :
JSS 1
Previous lesson :
The pupils have previous knowledge of various topics in their previous classes
Topic :
Counting of Number . Place Values Roman Figures
Behavioural objectives :
At the end of the lesson, the pupils should be able to
 Write figures in thousands , millions or billions
 expand any given numbers
 calculate the place values of any given number
 express Roman figures in Hindu Arabic numerals
 express figures in Roman figures
Instructional Materials :
 Wall charts
 Pictures
 Related Online Video
 Flash Cards
 Abacus
 Numeric Table Chart
Methods of Teaching :
 Class Discussion
 Group Discussion
 Asking Questions
 Explanation
 Role Modelling
 Role Delegation
Reference Materials :
 Scheme of Work
 Online Information
 Textbooks
 Workbooks
 9 Year Basic Education Curriculum
 Workbooks
Content :
WEEK ONE
TOPIC: WHOLE NUMBERS
CONTENT
 Introduction
 System of Counting
 Counting in Millions
 Counting in Billions and Trillions
INTRODUCTION
 Counting
It is likely that mathematics began when people started to count and measure. Counting and measuring are part of everyday life.
Ancient people used fingers and toes to help them count or group numbers in different number bases. This led them to collect numbers in groups: sometimes 5s (fingers of one hand), sometimes 10s (both hands) and even in 20s (hands and feet). When people group numbers in 5s, we say they use a base five method. The most common bases used were five, ten and twenty. For example, a person with thirty two cows would say ‘I have six fives and two cows’ when counting in base ten. The most widely used base is base ten also called the denary system.
Other bases of counting: seven and sixty
7 days = 1 week
60 seconds = 1 minute
60 minutes = 1 hour
In English, ‘dozen’ means 12, ‘score’ means 20 and ‘gross’ means 144
System of Counting
 Tally System
Tally marks were probably the first numerals.
The ancient people employed tally marks to count large numbers. The tally marks were scratched on stones or sometimes cut on sticks but today we use tally marks to count or record large data, especially in statistics.
A tally mark of 5 is written by putting a line across a tally count of 4.
i.e = 4 and = 5
Example 1
Draw the tally marks for each of the following numbers:
 34 (b) 15
Solution
 34 =
 15 =
EVALUATION
 During a dry season, it did not rain for 128 days. How many weeks and days is this?
 What is the number represented by
 Draw the tally marks for each of the following numbers: (a) 43 (b) 52
Roman numerals
The Romans used capital letters of the alphabets to represent numbers. Many people believe that the Romans used the fingers to represent numbers as follows:
I for one finger, II for two fingers, III for three fingers, V for five fingers and X for the combination of two hands ( or two V’s) .
The Roman also used L for fifty, C for hundred, D for five hundred and M for one thousand as shown below.
HinduArabic  Roman Numeral  HinduArabic  Roman Numeral 
1  I  20  XX 
2  II  40  XL 
3  III  50  L 
4  IV  60  LX 
5  V  90  XC 
6  VI  100  C 
7  VII  400  CD 
8  VIII  500  D 
9  IX  900  CM 
10  X  1000  M 
The Roman used the subtraction and addition method to obtain other numerals. For example
 IV means V I i.e. 5 4 = 4
 VI means V+ I, i.e. 5 + 1 = 6
 IX means X I, i.e. 10 – 1 = 9
 XXIV means XX + IV = 20 + 4 = 24
 CD means D C = 500 – 100 = 400
 MC means M + C = 1000 + 100 = 1100
Example 1
Change the following numbers to Roman numerals: (a) 2459 (b) 3282
Solution
 2459— 2000 = MM
400 = CD
50 = L
9 = IX
2459 = MMCDLIX
 3282 = 3000 + 200 + 80 + 2
= MMM CC LXXX II
i.e 3282 = MMMCCLXXXII
EVALUATION
 Write the following Roman figures in natural ( or counting) numbers:
 MMMCLIV (b) MMCDLXXI (c) MCMIX (d) DCCCIV
 Write the following natural numbers in Roman figures:
 2659 (b) 1009 (c) 3498 (d) 1584
 The Counting board
A counting board is a block of stone or wood ruled in columns. Loose counters, pebbles, stones or seeds in the columns show the value of the numbers in the columns.
Counters in the righthand column (U) represent units, counters in the next column (T) represent tens, and so on.
TH  H  T  U 
●●●  ●  
●●  ●●●●  ●●●● 
2 7 5
The diagram below is a counting board showing the number 275.
 The Abacus
An abacus is a frame consisting of beads or disks that can be moved up or down (i.e. slide) on a series of wires or strings. Each wire has its own value. Both abacus and counting board work in the same way when carrying out calculations.
Example 1
M HTH TH H T U
0
7
3
2
An Abacus showing 2703
 Place Value of Numbers
Numbers of units, tens, hundreds,…….., are each represented by a single numeral.
(a).For a whole number:
– the units place is at the righthand end of the number.
– the tens place is next to the units place on the left, and so on
For example: 5834 means ↓
5 thousands, 8 hundreds, 3 tens, and 4 units.
See the illustration below:
5 8 3 4
(b) for decimal fraction, we count the places to the right from the decimal point as tenths, hundredths, thousandths, etc.
See the illustration below:
↓ ↓ ↓ ↓ ↓
6 . 7 9 8
6 → units
. → decimal
7 → tenths
9 → hundredths
8 → thousandths
Example 1:
What is the place value of each of the following?
 the 9 in 10269
 the 2 in 2984
Solution:
 the 9 in 10269 is = 9 units or nine units
 the 2 in 2984 is = 2 thousands or two thousands
Example 2
What is the value of each of the following?
 the 8 in 1.85
 the 0 in 16.08
Solution:
 the 8 in 1.85 is = 8 tenths or eight tenths
 the 0 in 16.08 is =0 in tenths or zero tenths
Example 3
What is the value of each digit in 3 865 742
Solution
3  8  6  5  7  4  2  
M  H. Th  T.Th  Th  H  T  U  
Digit  Value  Word Form  
3  3 000 000  Three million  
8  800 000  Eight hundred thousand  
6  60 000  Sixty thousand  
5  5 000  Five thousand  
7  700  Seven hundred  
4  40  Forty  
2  2  Two 
EVALUATION
1 (a) The place value of 5 in 5763 is ……………
(b)What is the place value 1 in 5.691?
2. Give the value of each digit in 489 734
3. Write down the number shown in the following figures:
(a)
READING ASSIGNMENT


 Essential Mathematics for JSS1 by AJS Oluwasanmi page 37
 New General Mathematic for Jss1 by M. F. Macrae et al page 1718.

Counting and Writing in millions, billions and trillions
The figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits or units.
The table below gives the names and values of some large numbers.
Name  Value 
One thousand  1 000 
Ten thousand  10 000 
One hundred thousand  100 000 
One million  1 000 000 
Ten million  10 000 000 
One hundred million  100 000 000 
One billion  1 000 000 000 
One trillion  1 000 000 000 000 
Large numbers can be read easily by grouping the digits in threes starting from the right hand side as shown below.
Billion Million TH H T U
25 800 074 4 3 0
The 1^{st} gap separates hundreds from thousands and the second gap separates thousands from millions and the third gap separates million from billion.
Thus 25 800 074 430 reads twenty five billion, eight hundred million, seventy four thousand, eight hundred and ninety.
Example
Write the following in figures:
 twelve billion, three hundred and nine million, ninety five thousand, six hundred and sixty three
 six trillion, four hundred and thirty billion, one hundred and five million, two hundred and one thousand and fifty four
 nine hundred and four billion, five hundred and forty million, three hundred and seventy thousand, seven hundred and fifty
Solution
 You can work it out as follows:
Twelve billion  = 12 000 000 000 
Three hundred and nine million  = 309 000 000 
Ninety five thousand  = 95 000 
Six hundred and sixty three  = 663 
Adding  = 12 309 095 663 
Six Trillion  = 6 000 000 000 000 
Four hundred and thirty billion  = 430 000 000 000 
One hundred and five million  = 105 000 000 
Two hundred and one thousand  = 201 000 
Fifty four  = 54 
Adding  = 6 430 105 201 054 
Nine hundred and four billion  = 904 000 000 000 
Five hundred and forty million  = 540 000 000 
Three hundred and seventy thousand  = 370 000 
Seven hundred and fifty  = 750 
Adding  = 904 540 370 750 
EVALUATION
 Write the following in figures:
 Ninety nine million, eighty thousand, nine hundred and forty one.
 Fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.
 Write in figures, the number referred to in the statement: Last year a bank made a profit of ‘two hundred and twenty billion, five hundred and one thousand, four hundred and ninety three Naira ( N)
WEEKEND ASSIGNMENT
 The value of 8 in 18214 is (a) 8 units (b) 8 tens ( c) 8 hundreds ( d) 8 thousands (e) 8 ten thousands
 The Roman numerals CXCIV represents the number (a) 194 (b) 186 (c ) 214 (d) 215 (e) 216.
 What is the number represented by ? (a) 32 (b) 40 (c) 28 (d) 39
 The value of 7 in 3.673 is (a) 7tenths (b) 7 hundredths ( c ) 7 units ( d) 7 hundredth.
 Three million and four in figures is (a) 300004 (b) 300040 (c) 30000004 (d) 3000004
THEORY

 Change this Roman figure to natural numbers
(i) MMCDLXXI (ii) MMMCLIV
 Write the following in figures:
(a) fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.
(b) three hundred and twentynine billion, five hundred and sixty two million, eight hundred and one thousand, four hundred and thirty three.
Presentation
The topic is presented step by step
Step 1:
The class teacher revises the previous topics
Step 2.
He introduces the new topic
Step 3:
The class teacher allows the pupils to give their own examples and he corrects them when the needs arise
Conclusion
The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and where the needs arise.